1. Field of the Invention
This invention relates to a simulator which simulates, in real time, dynamic phenomena of a large scale electric power system, thereby analyzing them and further performing a function test of each element of the electric power system.
2. Description of Related Art
Heretofore two types of simulators are well-known which simulate an electric power system. One is an analog type which combines many of apparatuses each of which simulates each element of the electric power system, for example, such as shown in Kansai Electric Power Co's catalog "Advanced Power System Analyzer APSA", and the other is a digital type which analyzes each element by a large general-purpose computer by using a calculation equation.
However, the conventional analog type simulator can not simulate the real large scale electric power system and further a change of condition of the electric power system to be simulated is practically impossible because it requires enormous work loads. Explaining more concretely, the analog type simulator simulates the electric power system with a miniature model which is really provided with the electric power system elements such as generators, AVRs (Automatic Voltage Regulators), power generation control apparatuses like governors, transformers, loads, SVCs (Static Var Compensator), and transmission lines, thus as a scale of the electric power system to be simulated becomes larger, the miniature model occupies a larger space. For example, in order to simulate an electric power system including thirty generators, the above APSA occupies as large area as 700 m.sup.2 for only a simulator, thus there is a limit to an occupancy area for simulation of the large scale electric power system. Further, when changing wirings of the electric power system to be simulated, it is required to change connections of the simulator and this necessitates troublesome and a large quantity of work loads.
While the conventional digital type simulator has a few CPUs, in order to analyze differential equations for simulating elements such as a generator, excitation system, PSS (Power System Stabilizer), and governing system, the simulator employs either a batch solution which solves an equation expressing the whole system or a partition solution which solves serially each equation representing each element ("High Speed Transient Stability Calculation Method suitable for Array Processor", Institution of Electrical Engineers of Japan, treatises separate volume B, article No. 59-B36, pp297-304, May 1984).
However both the solutions consume much processing time because the batch solution is required to solve a large equation at one stroke, while the partition solution is required to stop all other processing to solve one equation during its solving, thus both the solutions can not cope with the simulation, in real time, of the real electric power system. Further, the digital type simulator calculates the differential equation to express the element of the electric power system as the case of the analog type simulator as mentioned above, but it is expected that because of necessary focusing calculation, an analysis of a high speed phenomenon is difficult to effect even with the decentralized computer, and further an error when modeling a real phenomenon in an equation can not be avoided.
Now, the simulation of an electric power system is a task of solving alternately two sets of equations in time series, that is, a differential equation that calculates dynamics of each element configuring the system such as a generator, excitation system, PSS, governing system and a rotating motion system, and a network equation that expresses a relation between a bus and a transmission line.
FIG. 1 is a flowchart showing whole of calculation processes of the electric power system simulator shown in the above "High Speed Transient Stability Calculating Method suitable for Array Processor".
Step S41 is a process of initialization, Step S21 to Step S23 are processes of electric power system network calculation, Step S101 to Step S105 are processes for generator dynamic characteristic calculation and Step S45 and Step S46 are processes proper to this technique.
Procedure of this flowchart is as follows.
First, after initialization in Step S41, calculation relating to a generator bus (Step S21) and calculation relating to a non-generator bus (Step S22) are executed respectively. In this flowchart, the electric power system network calculation is performed considering a so-called constant power characteristic of consuming a constant power rather than a non-linear characteristic of a load, for example, an applied voltage, thus a solution is obtained by repeated calculations as shown in Step S21 to Step S23. That is, focusing or non-focusing is decided in Step S23, and in the case of non-focusing, the process is returned to Step S21.
When focusing is decided in Step S23, a generator output power and terminal voltage are obtained. According to decisions in Step S45 and Step S46, when focusing for the second time or more, the process ends, and in other case (focusing for the first time), a generator dynamic characteristic is calculated using information on generator output power and terminal voltage in Step S101 to Step S105. That is, calculation of a rotating motion system (Step S101), calculation of PSS (Step S102), calculation of a excitation system (Step S103), calculation of a governing system (Step S104), and calculation of a generator equation (Step S105) are respectively performed. Using data of an amplitude and a phase of a generator internal induced voltage obtained from these calculations, the process is returned to Step S21 to perform again the electric power system network calculation.
In addition, in the flowchart of FIG. 1, the processes from "START" to "END" are performed in one time step of integration, and by cyclically repeating the process of every one time step of integration, a change of condition of the electric power system is serially calculated.
Now, in the calculation of the rotating motion system in Step S101, a generator rotor position .theta. is calculated by introducing a phase .delta. as a variable which meets an equation EQU .theta.=.omega..sub.0 t+.delta.
as shown, for example, in "Analytical Theory of Electric Power System" (pp 294-299, written by Sekine, published by Denki-Shoin in 1971), where .omega..sub.0 is a rated angular velocity in an A.C. system. In a usual A.C. system, all generators are rotating at an almost rated angular velocity, thus it is known that the phase .delta. remains within the range of -360 n.degree. to +360 n.degree. and there is no problem. However, when one generator causes, for example, step-out to increase a rotational speed or when the generator is in stopped condition, the phase .delta. rapidly increases or decreases. In this case, there arises no problem in pure theory, but a problem arises in a digital numerical calculation.
In a computer system, a numerical value is generally expressed with "A* 10.sup.B ", whereby the system usually handles numbers each of which combining a mantissa A and an exponent B. But hexadecimal numbers are actually used in the computer system, however, for simplification, the numerical calculation will be explained with decimal numbers.
For example, in the computer system handling a mantissa A of four digits and an exponent B of two digits, a decimal number "58325" is expressed as 5833*10.sup.1 and this is handled as a number "583301". Therefore, either the case where the phase .delta. is equal to "58325" or equal to "58333", both the numbers are handled as "583301" in the computer system. Thus, the difference between both the numbers is to be "8" in pure theory, but becomes "0" in the computer system. Therefore, when step-out or stop of a generator lasts long, the conventional digital type electric power system simulator sometimes handles data beyond the range of significant figures of the computer system as mentioned above and below comes unable to perform precise calculations and can not simulate the system.
As mentioned above, when simulation of condition of long-lasted generator step-out, simulation of a system including a stopped generator or simulation of a system including two different frequencies A.C. systems connected with a D.C. transmission system are performed by the conventional digital type electric power system simulator, the value of the phase .delta. becomes unusually large and falls within the range of a numerical calculation error of the computer system and this sometimes disables the computer system from calculation, that is, the simulation.
Further, in the conventional electric power system simulator, as shown in the flowchart of FIG. 1, repeated calculations are employed for the electric power system network calculation, thus extending an operation time, and a number of times of repetition until focusing differs depending on other condition, thereby causing a problem of an inconstant operation time. Therefore, it was difficult to perform, for example, the so-called real time simulation which advances calculation in a constant time interval. Further, in the so-called threshold running like the case of a voltage instability state, there are problems such that focusing ability is degraded to increase the number of times of calculation repetition and sometimes the case of non-focusing arises.
Further, in the conventional electric power system simulator performing the procedure of the flowchart of FIG. 1, all processings are executed by one calculating unit, thus time management, that is, processings in each predetermined time interval are relatively easily performed, but a time necessary for calculation is extended. As processings of Step S101 to Step S105 are required to be particularly performed on each generator, as a number of generators increases, a time of processings of Step S101 to Step S105 is more extended. In addition, there are problems such that, as the number of generators increases, the time management becomes more difficult and the real time simulation is disabled.
Now, as an application example of the aforementioned decentralized type computer, the invention disclosed in Japanese Patent Application No. 1-245493 (1989) is proposed as a digital type simulator capable of high speed processing.
In the invention disclosed in the Japanese Patent Application No. 1-245493 (1989), a decentralized type computer having a plurality of CPUs 61 is used as shown in FIG. 2 and a different equation expressing each element of the electric power system such as a generator, excitation system, PSS or a governing system is assigned to each one of the plurality of CPUs 61. Then each calculation processings divided into each element are decentralized-processed by each CPU 61, thereby the load of each CPU is alleviated, thus the calculations can be processed at a high speed as a whole.
By the way reference numeral 62 denotes a communication line connecting the space between respective CPUs 61.
FIG. 3 is a flowchart showing procedures relating to one bus which is one of the elements of the electric power system in the simulator of the invention disclosed in the above Japanese Patent Application No. 1-245493 (1989). By the way the bus includes a generator bus which is directly connected to the generator and a non-generator bus which is not directly connected to the generator.
As shown in FIG. 3, in a task of obtaining a solution of the different equation performed by each CPU 61, a task of calculation relating to electric systems of each generator bus 31 (PSS 33, excitation system 34, generator 35) and a task of calculation relating to mechanical systems of each generator bus 31 (rotating motion system 36, governing system 37) can be parallel-executed. However the task of calculation relating to each element of the electric system and that of the mechanical system are performed by CPUs 61 independently, thus data interchange is necessary between both the tasks. By the way processing on the non-generator bus 32 does not requires communication with a calculation task of dynamics of the generator bus 31.
In this way, a network equation 38 representative of a relation between the buses is calculated using results of the decentralized-processings of respective CPUs 61 and transferring data 39 between the buses until focusing at each CPU 61.
Now, in the conventional simulator using the above decentralized type computer, each different equation expressing each element of the electric power system is assigned to each CPU 61, whereby respective calculations on each element of the electric power system are decentralized to reduce a processing time. However, on the other hand, generally a solution of the network equation is obtained by solving system condition expressed by a linear equation with the LU analysis method or Newton-Raphson method. For example, generally regarding a generator and a load as equivalent current sources and expressing the system condition with the following linear equation system, EQU I=YV
where
I: current PA1 Y: admittance PA1 V: voltage
then the system condition is solved with the LU analysis method regarding the current I as a known quantity and the voltage V as an unknown quantity.
Besides other some algorithms are being considered which solve the equation with the decentralized type computer, but it is not right to say that high speed analysis capability of the decentralized system is best used even when any method is used.
In addition, the conventional digital type simulator has a problem in man-machine device. For example, the simulator can not output an intermediate result of an analysis calculation of the electric power system and has only a function of outputting the analysis result in a format of a table or graph only after the end of the calculation. This originates directly from logic unable to stop the analysis calculation or to intermediately output the calculation result, but besides that it is supposed that because of a low speed of the analysis calculation, an operator could not feel a real time sense and he did not also sense necessity of the man-machine device except output of the analysis result.